# Recitation 19: Common Emitter Ampliﬁer Review: Small signal model of BJT ```Recitation 19
Common Emitter Ampliﬁer
6.012 Spring 2009
Recitation 19: Common Emitter Ampliﬁer
Review: Small signal model of BJT
Low Frequency
Voltage/Current Controlled Current Source
gm =
γπ =
γo =
Ic
Ic
=
transconductance
Vth
kT /q
1
βF
=
gπ
gm
1
1
VA
=
base-width modulation
δic
go
IC
δVCE
High Frequency
Adding capacitances: between base-emitter, a forward-biased p-n junction
Cπ = depletion cap. + diﬀusion cap.
Between base-collector, reverse biased p-n junction
Cμ = depletion cap.
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Recitation 19
Common Emitter Ampliﬁer
6.012 Spring 2009
Transistor Ampliﬁers
Yesterday we started our discussion on transistor ampliﬁers. For ampliﬁers, we have:
Type
Voltage Ampliﬁer
Current Ampliﬁer
Transconductance Ampliﬁer
Transresistance Ampliﬁer
Input
V
I
V
I
Output
V
I
I
V
Voltage and transconductance ampliﬁers are most common. Yesterday, we discussed the
common-source ampliﬁer shown below:
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Recitation 19
Common Emitter Ampliﬁer
6.012 Spring 2009
Today, we will discuss common-emitter ampliﬁer (for the BJT version)
Resistor Bias
At Collector
Current Source
At Collector
For ampliﬁer circuits, what we are interested in are:
• What is the operating point? (Bias point)
• Signal Swing?
• Small signal gain; input resistance; output resistance
• Frequency Response
Among these, ﬁrst two are large signal analysis, while the last two are related to small
signal circuits.
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Recitation 19
Common Emitter Ampliﬁer
6.012 Spring 2009
DC Bias Point
For large signal analysis, Vs &amp; Rs will be gone. Also make RL ∞. See ﬁgure 4,
Vout = Vcc − Ic &middot; Rc
Vcc
If we choose Vout =
= 2.5 V (Vcc = 5 V), Rc = 10 kΩ
2
Vcc − Vout
5 V &middot; 2.5 V
Ic =
=
= 250 μA
Rc
10 kΩ
kT Ic
Ic = Is eqVBIAS /kT =⇒ VBIAS =
ln = 0.682 V
q
Is
Signal Swing
• Upswing limited by BJT going into cutoﬀ: Total signal Vout,max = Vcc
• Down swing limited by BJT going out of FAR into saturation Vout,min = VCE,SAT
Small Signal Analysis of CE Ampliﬁer
First obtain the small signal circuit of the circuit in Figure 4
• Short DC voltage bias
• Open DC circuit bias
Intrinsic will be (without Rs and RL )
This is a transconductance ampliﬁer, it turns out its small signal circuit is very similar to
the topography of our “two port model”
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Recitation 19
Common Emitter Ampliﬁer
6.012 Spring 2009
In comparison, we see
Rin = γπ
Gm = gm =
Ic
kT /q
Rout = γo ||Rc
Intrinsic or unloaded gain (short circuit output)
iout
Gm Vin
=
= Gm
Vin
Vin
iout
Vs
= Gm Vin &middot;
= Gm
Rout
Rout + RL
Rout
Rout+RL
1
Vs
Rin
γo ||Rc
γπ
Rin + Rs
&middot;
Vs = gm
γo ||Rc + RL
γπ + R
Vs
Replacing Rc with a Current Source
From the discussions in the above subsection, in general:
ro Rc =⇒ ro ||Rc = Rc
iout
Rc
rπ
and
= gm
&middot;
rπ + R s
vs
Rc + R L
If Rc RL or Rc &lt; RL , transconductance gain is degraded.
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Recitation 19
Common Emitter Ampliﬁer
6.012 Spring 2009
So we need a large Rout (output is a current)
=⇒ use a current source at the collector =⇒ Figure 5 can be a p-MOSFET, Rc → roc
(in small signal circuit, DC current is open)
On the CE Amp.
We consider the CE Amp. to be a transconductance ampliﬁer. In fact, it can also be just
a voltage ampliﬁer. In that case, the two port model becomes:
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Recitation 19
Common Emitter Ampliﬁer
6.012 Spring 2009
CS vs. CE Amp
In comparison with the CS Amp we discussed yesterday:
2I
D
• VBIAS = + VSS + VT
w
μn Cox
L
w
VDD
(by letting VOUT = 0, &amp; IR = ID =
μn Cox (VBIAS − VSS − VT )2 =
)
2L
RD
• VOUT,MAX = VDD (MOS into cutoﬀ)
VOUT,MIN = VBIAS − VT (MOSFET leave saturation)
• Rin = ∞, Rout = ro ||RD
AVD =
Vout
Vs
Vout
= −gm (ro ||RD )
Vin
= −gm (ro ||RD ||RL )
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6.012 Microelectronic Devices and Circuits
Spring 2009